Why is it when the screen to my device is off I do not receive any internet notifications?

Why when the screen on my device is off I do not receive email, messages from the chat service or anything else from the Internet. Only when I pick up the phone and turn the screen, messages arrive. Otherwise, I use wi-fi. Can I do it through my adjustment device to fix? I use Blu Dash JR. In advanced settings I have WLAN sleep policy-specify when to switch from wlan to mobile data(when screen turns off, never when plugged in and never). And nothing else. This is so lame for a smart device, can anibody help me? Thanks